Seismic data is collected to analyze the subsurface of the Earth, and is particularly collected in connection with hydrocarbon exploration and production activities. Seismic data for analyzing subsurface structures may be collected on land or over water. In order to obtain seismic data, an acoustic source is used which typically consists of explosives or a seismic vibrator on land or an impulse of compressed air at sea. The seismic signals reflected by the various geologic layers beneath the surface of the Earth are known as traces and are sensed by a large number, typically hundreds or thousands, of sensors such as geophones on land and hydrophones at sea. The reflected signals are recorded and the results are analyzed to derive an indication of the geology in the subsurface. Such indications may then be used to assess the likelihood and location of potential hydrocarbon deposits.
Seismic surveys are generally conducted using one or more receiver lines having a plurality of receiver station locations spaced evenly along their lengths. In a two dimensional (2D) survey, a single receiver line is used and the acoustic source is typically positioned at various points in-line with the receiver line. In a three dimensional survey, a plurality of parallel receiver lines are typically used and the acoustic source is generally positioned at various points offset from the receiver lines. While a 2D seismic survey can only create a cross-sectional representation of the subsurface, a 3D seismic survey can be used to develop a three dimensional representation of the subsurface.
Seismic data are subject to a wide variety of noise related problems that can and do limit its usefulness. Broadly speaking, noise found in seismic traces is either incoherent or coherent. Incoherent ambient noise, or uncorrelated “white” noise, is ubiquitous and is generally greatly attenuated through the simple expedient of stacking, although extremely large individual data values (“spikes”) and “bad” traces often need special attention. Coherent, or correlated, noise on the other hand cannot usually be so readily eliminated. Some common examples of coherent noise include multiple reflections, ground roll, air waves, guided waves, sideswipe, cable noise and 60 hertz power line noise. Among the many known approaches to attenuating noise, there are space-time based or transform based methods. Space-time based methods operate on the time series of the acquired data. Transform based methods operate on data transformed from the space-time domain into another domain using a suitable transformation. The most popular of the 2-D transform methods is the 2-D Fourier transform (or “f-k” transform). Seismic data containing noise are transformed to the alternative domain where noise events are more compactly represented. If the noise energy can be located and isolated in the transform domain, it is removed from the transformed data by filtering or muting, i.e. by setting the values in the region corresponding to the noise energy equal to zero or some other minimal value. Finally, the transformed data, without the noise energy, are then inverse transformed to return them to the time and offset (i.e., untransformed or “x-t”) domain.
In conventional seismic data acquisition systems data are inherently filtered through use of “hard-wired” (electrically connected) groups of sensors. A group or receiver array delivers a single output trace (the normalized sum or arithmetic average of the output of all individual sensors of the group) at the particular receiver station location about which the sensors are placed. The single trace is the normalized sum or arithmetic average of the output of all individual sensors making up the group. Without further processing, such a two-dimensional group has a spectral response that can be approximated by a frequency- independent 2D sinc function in the wavenumber or kx-ky domain.
More recently, however, seismic surveys have been performed using single or point receiver arrays. Such surveys offer the potential of recording the output of individual sensors or receivers and the inherent filtering effect of the hard-wired group can be replaced by filters that are better adapted to the nature of seismic noise and preserve more of the seismic reflection signals.
It is therefore an object of the present invention to provide methods for processing seismic data, particularly methods for designing and applying filters for such data.